"I just got my brand new Pulse Radeon RX 580 8GB video card from a company out of Chicago called CDW. (Computer Discount Warehouse?) The card cost me about $390 with the tax and shipping. I think I got lucky because many of these cards are selling for $500+.(I assume it's the Sapphire Pulse Radeon RX 580 8GD5.)

The Pulse Radeon RX 580 8GB works on the Mac Pro 2009-2012 OOTB. The drivers were built into Sierra & High Sierra. It is essential (IMHO) to use the SwitchResX app to set your Resolution to the desired 4k or 5k monitors, which (in my case) is scaled at 2560X1440@ 60hz. (He's using an LG 32UD59-B 4K 32in Display, scaled due to the menu text size at 3840x2160 native rez.)

In the About this Mac in Sierra 10.12.6 it will show up as an AMD R9 xxx 8192 MB. In High Sierra you will see the full name correctly. There are no problems at start-up. You will see a brief start-up screen and then right to your log-in. It's great and fast.
(Also shows as "Metal Supported")

I don't have a lot of ways to measure this cards performance, but Cinebench R15 is giving me almost 66fps, and Geek Bench 4 OpenCL Score is 134379. That is up from 107000 when using the Radeon R9 280X 3GB card. This card is in the ballpark of the GeForce GTX 1070 Ti. Just as fast as the GeForce Video Card on my Mac in many ways.(Having native driver support is a plus, where Nvidia's web drivers need updates for each macOS update, although Nvidia has been pretty quick to post web driver updates. Nvidia also has CUDA support, but personally I don't have experience with it.-M)

Interesting upgrade and a very pleasant surprise.

(I asked to confirm it wasn't flashed.)
This card was right out of the box and not flashed.
The Pulse Radeon RX 580 was a card that Apple approved for the developers for Beta testing Sierra and High Sierra. For one reason or the other this card just works. Obviously, the drivers are there. I cannot guarantee that any other Radeon 580 card (such as, Nitro) will work OOTB on a Mac. I did a lot of research to make sure I was buying a Sapphire Pulse Radeon RX 580 8GB video card that would work OOTB on a Mac.

I can't say how much of the start up I am seeing, since I have an SSD Drive. My start up is really fast. Then, the log-in comes up.

This card has performed perfectly over the last 48 hours. I know there are quite a few Mac Pro owners using this card. It's a great gaming card.

(he later wrote)
In Cinebench there's only about 1 FPS difference between this card and the R9 280X. However, under certain circumstances the RX 580 will far exceed the R9 280X. This is a gaming card and a card for Digital Video Editing and Rendering.

If you know anyone that wants a Radeon R9 280X 3GB card (flashed) and perfect for 4K monitors, let me know. It's $250 with cables included and (CONUS) shipping. I also have the (Mac) ATI Radeon HD 5770 1GB for $150 (CONUS) shipping included.
Thanks for everything.
-Jman"

He also sent lots of screenshots of GeekBench, CineBench, System Info, etc. that I'll add later (or summarize scores from the larger images).